Instructor: Dr. Gábor Lippner
Text: handouts and Miklós Bóna: A walk through combinatorics
Basic counting rules (product rule, sum rule, permutations, combinations, Pascal's triangle, occupancy problems, distribution problems, Stirling numbers).
Generating functions (definition, operations on generating functions,
applications to counting, binomial theorem,
exponential generating functions).
Recurrences (Fibonacci numbers, derangements, the method of generating functions).
Principle of inclusion and exclusion (the principle and applications,
occupancy problems with distinguishable balls and
Introductory graph theory (quick overview of fundamental concepts, connectedness, graph coloring, trees).
Pigeonhole principle and Ramsey theory (Ramsey's theorem, bounds on Ramsey numbers, applications).